Existence And Stability Of Vortex Solitons In Photorefractive Optical Lattices

In nonlinear media,optical solitons are non-diffraction waves caused by a cancellation of nonlinear response of the media to the light and diffraction effects.In self-focusing homogeneous medium,the beams will widen in natural due to the diffraction effect,and solitons could only be found in self-focusing medium.Some kinds of solitons like vortex solitons are instable in homogeneous medium due to the azimuthal modulational instability.Photonic lattices(e.g.a periodic structure of refractive index modulation)result in unique photonic band-gap structure similar to Bloch bands in solid-state physics,which can cause bragg reflection and anomalous diffractions to a given light beam.So self-defocusing gap solitons can exist in photonic lattices,which enrich the search in optical solitons.In this paper,we investigate the existence and stability of vortex solitons in photorefractive optical lattices by numerical simulation.The main contents and achievements are as follows:1.We report the existence and stability of 1-charge discrete vortex solitons in linear scaled-space square lattices with photorefractive self-focusing nonlinearity.By scaling the square lattice along edge and diagonal,we obtain rectangle and diamond lattices.In rectangle lattices,the structure of rectangle potential strongly affects the profile of vortex solitons,leading to distinct intensity asymmetric,phase dislocation,and exponentially instabilities for low power instable vortices.In contrast,vortex profile could be well hold in diamond lattices,and the phase difference can be hold in ?/2 between every two neighbor main lobes.According to the results of linear stability analysis,low power vortices process exponentially instabilities modes in rectangle lattices.However,the low power instable vortices in diamond lattices instable vortices have a weaker instability than in rectangle lattices,and the growth rates are one magnitude less than in rectangle lattices.2.We studied the existence and stability of vortex solitons in Lieb-like photonic lattices in photorefractive self-focusing nonlinearity medium.By dividing three lattice points in minimum periodic units of the Lieb lattice into two groups and changing the relative intensity of the two groups of lattice,we open the first and second band gaps which are closing in the natural Lieb lattice.Based on this idea,we study the stability of the fundamental soliton and the vortex soliton in band gaps and semi-infinite band.For fundamental soliton,we find that the fundamental soliton with moderate energy is stable in the second band gap.The on-site incidence vortex solitons are unstable in the first band gap.Instead,the off-site incidence vortex solitons are stable at suitable energy,and process small growth rates in the whole first gap.